The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  X  1  X
 0 X^2+2  0  0  0 X^2 X^2+2 X^2  2  2  0 X^2+2 X^2  2 X^2 X^2+2  0 X^2+2 X^2 X^2  0 X^2 X^2  2  2  0  0 X^2 X^2+2 X^2+2  2
 0  0 X^2+2  0 X^2 X^2 X^2  0  2 X^2  2 X^2  0 X^2+2 X^2  2  2  2 X^2+2 X^2+2  2 X^2+2  0  0 X^2+2 X^2+2  0  2  2 X^2+2  2
 0  0  0 X^2+2 X^2  0 X^2+2 X^2+2  2 X^2 X^2  2 X^2  0 X^2+2  2 X^2+2 X^2+2  0 X^2  0 X^2+2  2 X^2+2 X^2+2 X^2 X^2 X^2+2  2  0 X^2+2

generates a code of length 31 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+121x^28+248x^30+256x^31+338x^32+8x^34+51x^36+1x^56

The gray image is a code over GF(2) with n=248, k=10 and d=112.
This code was found by Heurico 1.16 in 0.125 seconds.